<!-- build time:Wed Jun 21 2023 22:33:34 GMT+0800 (GMT+08:00) --><!DOCTYPE html><html lang="zh-CN"><head><meta charset="UTF-8"><meta name="viewport" content="width=device-width,initial-scale=1,maximum-scale=2"><meta name="theme-color" content="#FFF"><meta name="baidu-site-verification" content="code-C0oocRvMWv"><link rel="apple-touch-icon" sizes="180x180" href="/images/apple-touch-icon.png"><link rel="icon" type="image/ico" sizes="32x32" href="/images/favicon.ico"><link rel="mask-icon" href="/images/logo.svg" color=""><link rel="manifest" href="/images/manifest.json"><meta name="msapplication-config" content="/images/browserconfig.xml"><meta http-equiv="Cache-Control" content="no-transform"><meta http-equiv="Cache-Control" content="no-siteapp"><meta name="baidu-site-verification" content="https://jiang-hs.gitee.io"><link rel="alternate" type="application/rss+xml" title="航 順" href="https://jiang-hs.gitee.io/rss.xml"><link rel="alternate" type="application/atom+xml" title="航 順" href="https://jiang-hs.gitee.io/atom.xml"><link rel="alternate" type="application/json" title="航 順" href="https://jiang-hs.gitee.io/feed.json"><link rel="stylesheet" href="//fonts.googleapis.com/css?family=Mulish:300,300italic,400,400italic,700,700italic%7CFredericka%20the%20Great:300,300italic,400,400italic,700,700italic%7CNoto%20Serif%20JP:300,300italic,400,400italic,700,700italic%7CNoto%20Serif%20SC:300,300italic,400,400italic,700,700italic%7CInconsolata:300,300italic,400,400italic,700,700italic&display=swap&subset=latin,latin-ext"><link rel="stylesheet" href="/css/app.css?v=0.0.0"><meta name="keywords" content="推荐系统,新闻推荐,论文精读,隐私保护,无目标攻击"><link rel="canonical" href="https://jiang-hs.gitee.io/posts/cc988ffe/"><meta name="description" content="新闻推荐是个性化新闻发布的关键。联邦新闻推荐支持从许多客户端学习协作模型，而无需共享其原始数据。它在保护隐私的新闻推荐方面很有前景。然而，联合新闻推荐的安全性仍不清楚。本文提出一种称为 UA-FedRec 的非目标攻击来研究这个问题。通过利用新闻推荐和联邦学习的先验知识，UA-FedRec 可以在很小比例的恶意客户端情况下有效地降低模型性能。首先，新闻推荐的有效性高度依赖于用户建模和新闻建模。文"><meta property="og:type" content="article"><meta property="og:title" content="UA-FedRec：对联邦新闻推荐的无目标攻击"><meta property="og:url" content="https://jiang-hs.gitee.io/posts/cc988ffe/index.html"><meta property="og:site_name" content="航 順"><meta property="og:description" content="新闻推荐是个性化新闻发布的关键。联邦新闻推荐支持从许多客户端学习协作模型，而无需共享其原始数据。它在保护隐私的新闻推荐方面很有前景。然而，联合新闻推荐的安全性仍不清楚。本文提出一种称为 UA-FedRec 的非目标攻击来研究这个问题。通过利用新闻推荐和联邦学习的先验知识，UA-FedRec 可以在很小比例的恶意客户端情况下有效地降低模型性能。首先，新闻推荐的有效性高度依赖于用户建模和新闻建模。文"><meta property="og:locale" content="zh_CN"><meta property="og:image" content="https://shun309.oss-cn-hangzhou.aliyuncs.com/photos/20230420140544.png"><meta property="og:image" content="https://shun309.oss-cn-hangzhou.aliyuncs.com/photos/20230130175622.png"><meta property="article:published_time" content="2023-04-12T01:40:08.000Z"><meta property="article:modified_time" content="2023-04-21T06:01:13.404Z"><meta property="article:author" content="hang shun"><meta property="article:tag" content="推荐系统"><meta property="article:tag" content="新闻推荐"><meta property="article:tag" content="论文精读"><meta property="article:tag" content="隐私保护"><meta property="article:tag" content="无目标攻击"><meta name="twitter:card" content="summary"><meta name="twitter:image" content="https://shun309.oss-cn-hangzhou.aliyuncs.com/photos/20230420140544.png"><title>UA-FedRec：对联邦新闻推荐的无目标攻击 - 隐私保护新闻推荐 - 新闻推荐 - 论文精读 | hang shun = 航 順 = 天官赐福，百无禁忌</title><meta name="generator" content="Hexo 5.4.2"></head><body itemscope itemtype="http://schema.org/WebPage"><div id="loading"><div class="cat"><div class="body"></div><div class="head"><div class="face"></div></div><div class="foot"><div class="tummy-end"></div><div class="bottom"></div><div class="legs left"></div><div class="legs right"></div></div><div class="paw"><div class="hands left"></div><div class="hands right"></div></div></div></div><div id="container"><header id="header" itemscope itemtype="http://schema.org/WPHeader"><div class="inner"><div id="brand"><div class="pjax"><h1 itemprop="name headline">UA-FedRec：对联邦新闻推荐的无目标攻击</h1><div class="meta"><span class="item" title="创建时间：2023-04-12 09:40:08"><span class="icon"><i class="ic i-calendar"></i> </span><span class="text">发表于</span> <time itemprop="dateCreated datePublished" datetime="2023-04-12T09:40:08+08:00">2023-04-12</time> </span><span class="item" title="本文字数"><span class="icon"><i class="ic i-pen"></i> </span><span class="text">本文字数</span> <span>5.2k</span> <span class="text">字</span> </span><span class="item" title="阅读时长"><span class="icon"><i class="ic i-clock"></i> </span><span class="text">阅读时长</span> <span>5 分钟</span></span></div></div></div><nav id="nav"><div class="inner"><div class="toggle"><div class="lines" aria-label="切换导航栏"><span class="line"></span> <span class="line"></span> <span class="line"></span></div></div><ul class="menu"><li class="item title"><a href="/" rel="start">hang shun</a></li></ul><ul class="right"><li class="item theme"><i class="ic i-sun"></i></li><li class="item search"><i class="ic i-search"></i></li></ul></div></nav></div><div id="imgs" class="pjax"><ul><li class="item" data-background-image="https://pic1.imgdb.cn/item/64427ca20d2dde5777b04d90.png"></li><li class="item" data-background-image="https://pic1.imgdb.cn/item/60d7f97b5132923bf8a9b545.jpg"></li><li class="item" data-background-image="https://pic1.imgdb.cn/item/60d7f93d5132923bf8a86d6c.jpg"></li><li class="item" data-background-image="https://pic1.imgdb.cn/item/60d7f98e5132923bf8aa23d2.jpg"></li><li class="item" data-background-image="https://pic1.imgdb.cn/item/60d7f96c5132923bf8a96918.jpg"></li><li class="item" data-background-image="https://pic1.imgdb.cn/item/60d7f98e5132923bf8aa237d.jpg"></li></ul></div></header><div id="waves"><svg class="waves" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" viewBox="0 24 150 28" preserveAspectRatio="none" shape-rendering="auto"><defs><path id="gentle-wave" d="M-160 44c30 0 58-18 88-18s 58 18 88 18 58-18 88-18 58 18 88 18 v44h-352z"/></defs><g class="parallax"><use xlink:href="#gentle-wave" x="48" y="0"/><use xlink:href="#gentle-wave" x="48" y="3"/><use xlink:href="#gentle-wave" x="48" y="5"/><use xlink:href="#gentle-wave" x="48" y="7"/></g></svg></div><main><div class="inner"><div id="main" class="pjax"><div class="article wrap"><div class="breadcrumb" itemscope itemtype="https://schema.org/BreadcrumbList"><i class="ic i-home"></i> <span><a href="/">首页</a></span><i class="ic i-angle-right"></i> <span itemprop="itemListElement" itemscope itemtype="https://schema.org/ListItem"><a href="/categories/%E8%AE%BA%E6%96%87%E7%B2%BE%E8%AF%BB/" itemprop="item" rel="index" title="分类于 论文精读"><span itemprop="name">论文精读</span></a><meta itemprop="position" content="1"></span><i class="ic i-angle-right"></i> <span itemprop="itemListElement" itemscope itemtype="https://schema.org/ListItem"><a href="/categories/%E8%AE%BA%E6%96%87%E7%B2%BE%E8%AF%BB/%E6%96%B0%E9%97%BB%E6%8E%A8%E8%8D%90/" itemprop="item" rel="index" title="分类于 新闻推荐"><span itemprop="name">新闻推荐</span></a><meta itemprop="position" content="2"></span><i class="ic i-angle-right"></i> <span class="current" itemprop="itemListElement" itemscope itemtype="https://schema.org/ListItem"><a href="/categories/%E8%AE%BA%E6%96%87%E7%B2%BE%E8%AF%BB/%E6%96%B0%E9%97%BB%E6%8E%A8%E8%8D%90/%E9%9A%90%E7%A7%81%E4%BF%9D%E6%8A%A4%E6%96%B0%E9%97%BB%E6%8E%A8%E8%8D%90/" itemprop="item" rel="index" title="分类于 隐私保护新闻推荐"><span itemprop="name">隐私保护新闻推荐</span></a><meta itemprop="position" content="3"></span></div><article itemscope itemtype="http://schema.org/Article" class="post block" lang="zh-CN"><link itemprop="mainEntityOfPage" href="https://jiang-hs.gitee.io/posts/cc988ffe/"><span hidden itemprop="author" itemscope itemtype="http://schema.org/Person"><meta itemprop="image" content="/images/avatar.jpg"><meta itemprop="name" content="hang shun"><meta itemprop="description" content="天官赐福，百无禁忌, 世中逢尔，雨中逢花"></span><span hidden itemprop="publisher" itemscope itemtype="http://schema.org/Organization"><meta itemprop="name" content="航 順"></span><div class="body md" itemprop="articleBody"><p><img data-src="https://shun309.oss-cn-hangzhou.aliyuncs.com/photos/20230420140544.png" alt="" width="75%"></p><p>新闻推荐是个性化新闻发布的关键。联邦新闻推荐支持从许多客户端学习协作模型，而无需共享其原始数据。它在保护隐私的新闻推荐方面很有前景。然而，联合新闻推荐的安全性仍不清楚。本文提出一种称为 UA-FedRec 的非目标攻击来研究这个问题。通过利用新闻推荐和联邦学习的先验知识，UA-FedRec 可以在很小比例的恶意客户端情况下有效地降低模型性能。首先，新闻推荐的有效性高度依赖于用户建模和新闻建模。文章设计了一种新闻相似度摄动方法，使相似新闻的表示更远，不相似新闻的表示更接近于中断新闻建模，并提出了一种用户模型摄动方法，使恶意用户更新与良性更新的相反方向中断用户建模。其次，来自不同客户端的更新通常根据其样本量进行加权平均。文章提出了一种数量摄动的方法，将恶意客户端样本大小扩大到一个合理的范围，以放大恶意更新的影响。在两个真实数据集上的大量实验表明，即使在应用防御的情况下，UA-FedRec 也能有效地降低现有联邦新闻推荐方法的准确性。本文的研究揭示了现有联邦新闻推荐系统中一个关键的安全问题，并呼吁研究努力解决这个问题。</p><h1 id="问题表述"><a class="anchor" href="#问题表述">#</a> 问题表述</h1><p>将新闻数据集表示为<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="script">N</mi><mo>=</mo><mo stretchy="false">{</mo><msub><mi>𝑛</mi><mn>1</mn></msub><mo separator="true">,</mo><msub><mi>𝑛</mi><mn>2</mn></msub><mo separator="true">,</mo><mi mathvariant="normal">.</mi><mi mathvariant="normal">.</mi><mi mathvariant="normal">.</mi><msub><mi>𝑛</mi><mi>𝐿</mi></msub><mo stretchy="false">}</mo></mrow><annotation encoding="application/x-tex">\mathcal N = \{ 𝑛_1,𝑛_2,...𝑛_𝐿 \}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:.68333em;vertical-align:0"></span><span class="mord mathcal" style="margin-right:.14736em">N</span><span class="mspace" style="margin-right:.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-.25em"></span><span class="mopen">{</span><span class="mord"><span class="mord mathnormal">n</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:.15em"><span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:.16666666666666666em"></span><span class="mord"><span class="mord mathnormal">n</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:.15em"><span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:.16666666666666666em"></span><span class="mord">.</span><span class="mord">.</span><span class="mord">.</span><span class="mord"><span class="mord mathnormal">n</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:0;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">L</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:.15em"><span></span></span></span></span></span></span><span class="mclose">}</span></span></span></span>，其中<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>𝐿</mi></mrow><annotation encoding="application/x-tex">𝐿</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:.68333em;vertical-align:0"></span><span class="mord mathnormal">L</span></span></span></span>为新闻条数。每一条新闻<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>𝑛</mi><mi>𝑖</mi></msub></mrow><annotation encoding="application/x-tex">𝑛_𝑖</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:.58056em;vertical-align:-.15em"></span><span class="mord"><span class="mord mathnormal">n</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:0;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:.15em"><span></span></span></span></span></span></span></span></span></span>都以标题<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>t</mi><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">t_i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:.76508em;vertical-align:-.15em"></span><span class="mord"><span class="mord mathnormal">t</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:0;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:.15em"><span></span></span></span></span></span></span></span></span></span> 表示。将参与模型训练的全部客户端表示为<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="script">U</mi><mo>=</mo><mo stretchy="false">{</mo><msub><mi>u</mi><mn>1</mn></msub><mo separator="true">,</mo><msub><mi>u</mi><mn>2</mn></msub><mo separator="true">,</mo><mi mathvariant="normal">.</mi><mi mathvariant="normal">.</mi><mi mathvariant="normal">.</mi><msub><mi>u</mi><mi>N</mi></msub><mo stretchy="false">}</mo></mrow><annotation encoding="application/x-tex">\mathcal U = \{ u_1,u_2,...u_N \}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:.68333em;vertical-align:0"></span><span class="mord mathcal" style="margin-right:.09931em">U</span><span class="mspace" style="margin-right:.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-.25em"></span><span class="mopen">{</span><span class="mord"><span class="mord mathnormal">u</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:.15em"><span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:.16666666666666666em"></span><span class="mord"><span class="mord mathnormal">u</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:.15em"><span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:.16666666666666666em"></span><span class="mord">.</span><span class="mord">.</span><span class="mord">.</span><span class="mord"><span class="mord mathnormal">u</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:0;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:.10903em">N</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:.15em"><span></span></span></span></span></span></span><span class="mclose">}</span></span></span></span> 作为，其中<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>𝑁</mi></mrow><annotation encoding="application/x-tex">𝑁</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:.68333em;vertical-align:0"></span><span class="mord mathnormal" style="margin-right:.10903em">N</span></span></span></span>是客户端数量。给定用户<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>𝑢</mi><mi>𝑗</mi></msub></mrow><annotation encoding="application/x-tex">𝑢_𝑗</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:.716668em;vertical-align:-.286108em"></span><span class="mord"><span class="mord mathnormal">u</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:.311664em"><span style="top:-2.5500000000000003em;margin-left:0;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:.05724em">j</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:.286108em"><span></span></span></span></span></span></span></span></span></span>，他的私人点击数据<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>B</mi><mi>𝑗</mi></msub></mrow><annotation encoding="application/x-tex">B_𝑗</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:.969438em;vertical-align:-.286108em"></span><span class="mord"><span class="mord mathnormal" style="margin-right:.05017em">B</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:.311664em"><span style="top:-2.5500000000000003em;margin-left:-.05017em;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:.05724em">j</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:.286108em"><span></span></span></span></span></span></span></span></span></span>存储在他的本地设备中。在联邦新闻推荐中，这些<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>𝑁</mi></mrow><annotation encoding="application/x-tex">𝑁</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:.68333em;vertical-align:0"></span><span class="mord mathnormal" style="margin-right:.10903em">N</span></span></span></span>个客户端协作训练全局新闻推荐模型<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">Θ</mi></mrow><annotation encoding="application/x-tex">\Theta</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:.68333em;vertical-align:0"></span><span class="mord">Θ</span></span></span></span>。<strong>在每一轮中，中央服务器随机选择<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>𝑘</mi></mrow><annotation encoding="application/x-tex">𝑘</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:.69444em;vertical-align:0"></span><span class="mord mathnormal" style="margin-right:.03148em">k</span></span></span></span>个客户端。每个所选客户端用其本地数据集训练其本地新闻推荐模型。更新后的模型与从服务器接收到的全局模型的差值记为模型更新</strong><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>g</mi></mrow><annotation encoding="application/x-tex">g</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:.625em;vertical-align:-.19444em"></span><span class="mord mathnormal" style="margin-right:.03588em">g</span></span></span></span>。模型更新由选定的客户端上传，并由中央服务器进一步聚合。在这些<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>𝑁</mi></mrow><annotation encoding="application/x-tex">𝑁</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:.68333em;vertical-align:0"></span><span class="mord mathnormal" style="margin-right:.10903em">N</span></span></span></span>个客户端中，本文假设存在由攻击者控制的恶意客户端<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>𝑚</mi></mrow><annotation encoding="application/x-tex">𝑚</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:.43056em;vertical-align:0"></span><span class="mord mathnormal">m</span></span></span></span>。恶意客户端被表示为<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi mathvariant="script">U</mi><mi>m</mi></msub><mo>=</mo><mo stretchy="false">{</mo><msub><mi>u</mi><mn>1</mn></msub><mo separator="true">,</mo><msub><mi>u</mi><mn>2</mn></msub><mo separator="true">,</mo><mi mathvariant="normal">.</mi><mi mathvariant="normal">.</mi><mi mathvariant="normal">.</mi><msub><mi>u</mi><mi>m</mi></msub><mo stretchy="false">}</mo><mo>⊆</mo><mi mathvariant="script">U</mi></mrow><annotation encoding="application/x-tex">\mathcal U_m = \{ u_1,u_2,...u_m \}\subseteq \mathcal U</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:.83333em;vertical-align:-.15em"></span><span class="mord"><span class="mord mathcal" style="margin-right:.09931em">U</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:.151392em"><span style="top:-2.5500000000000003em;margin-left:-.09931em;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-.25em"></span><span class="mopen">{</span><span class="mord"><span class="mord mathnormal">u</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:.15em"><span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:.16666666666666666em"></span><span class="mord"><span class="mord mathnormal">u</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:.15em"><span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:.16666666666666666em"></span><span class="mord">.</span><span class="mord">.</span><span class="mord">.</span><span class="mord"><span class="mord mathnormal">u</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:.151392em"><span style="top:-2.5500000000000003em;margin-left:0;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:.15em"><span></span></span></span></span></span></span><span class="mclose">}</span><span class="mspace" style="margin-right:.2777777777777778em"></span><span class="mrel">⊆</span><span class="mspace" style="margin-right:.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:.68333em;vertical-align:0"></span><span class="mord mathcal" style="margin-right:.09931em">U</span></span></span></span> 。攻击者的目标是通过从选定的恶意客户端上传恶意模型更新<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>g</mi><mi>m</mi></msup></mrow><annotation encoding="application/x-tex">g^m</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:.858832em;vertical-align:-.19444em"></span><span class="mord"><span class="mord mathnormal" style="margin-right:.03588em">g</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:.664392em"><span style="top:-3.063em;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">m</span></span></span></span></span></span></span></span></span></span></span> 来降低生成的全局模型对任何输入样本的性能。</p><h1 id="威胁模型"><a class="anchor" href="#威胁模型">#</a> 威胁模型</h1><p><strong>攻击者的目标</strong>：攻击者的目标是降低联邦新闻推荐系统对任意输入样本的性能，即，它是对联邦新闻推荐系统的无目标攻击。</p><p><strong>攻击者的能力</strong>：在参与模型训练的客户端中存在由攻击者<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>m</mi></mrow><annotation encoding="application/x-tex">m</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:.43056em;vertical-align:0"></span><span class="mord mathnormal">m</span></span></span></span> 控制的恶意客户端<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>𝑁</mi></mrow><annotation encoding="application/x-tex">𝑁</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:.68333em;vertical-align:0"></span><span class="mord mathnormal" style="margin-right:.10903em">N</span></span></span></span>。由于推荐系统在实践中通常有数百万用户，因此本文认为恶意客户端的合理百分比应该达到 1%。攻击者可以操纵恶意客户端的模型更新来降低全局模型的性能。</p><p><strong>攻击者的知识</strong>：本文假设攻击者在恶意客户端的设备上拥有对代码、本地模型和良性数据集的完全访问权限。另外，本文假设攻击者拥有所有新闻的信息，例如新闻标题。由于联邦新闻推荐中的客户端并不共享其本地数据，因此本文假设攻击者仅对数据分布有部分了解。由于服务器可能不会发布其聚合代码，本文<strong>假设攻击者不知道服务器使用的聚合规则</strong>。同时，本文假设恶意客户端可以进行通信和协作来攻击全局推荐模型。</p><h1 id="基本新闻推荐模型"><a class="anchor" href="#基本新闻推荐模型">#</a> 基本新闻推荐模型</h1><p>FedRec 与大多数新闻推荐模型兼容。一般来说，本文的 UA-FedRec 不知道新闻推荐模型结构。新闻推荐模型一般由三个核心组件组成：新闻模型、用户模型和点击预测模型。给定一条新闻<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>𝑛</mi></mrow><annotation encoding="application/x-tex">𝑛</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:.43056em;vertical-align:0"></span><span class="mord mathnormal">n</span></span></span></span>，新闻模型从新闻标题生成新闻表示<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>n</mi></mrow><annotation encoding="application/x-tex">n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:.43056em;vertical-align:0"></span><span class="mord mathnormal">n</span></span></span></span>。本文将在 NRMS 和 LSTUR 两个模型上进行实验。</p><ul><li>在 NRMS 中，新闻模型采用多头自注意力网络和附加注意力层相结合的方式实现。</li><li>在 LSTUR 中，新闻模型由卷积网络和附加注意力层组成。</li></ul><p>给定用户<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>u</mi></mrow><annotation encoding="application/x-tex">u</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:.43056em;vertical-align:0"></span><span class="mord mathnormal">u</span></span></span></span> 的历史新闻表示<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">[</mo><msub><mi>n</mi><mn>1</mn></msub><mo separator="true">,</mo><msub><mi>n</mi><mn>2</mn></msub><mi mathvariant="normal">.</mi><mi mathvariant="normal">.</mi><mi mathvariant="normal">.</mi><msub><mi>n</mi><mi>𝑠</mi></msub><mo stretchy="false">]</mo></mrow><annotation encoding="application/x-tex">[n_1,n_2...n_𝑠]</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-.25em"></span><span class="mopen">[</span><span class="mord"><span class="mord mathnormal">n</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:.15em"><span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:.16666666666666666em"></span><span class="mord"><span class="mord mathnormal">n</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:.15em"><span></span></span></span></span></span></span><span class="mord">.</span><span class="mord">.</span><span class="mord">.</span><span class="mord"><span class="mord mathnormal">n</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:.151392em"><span style="top:-2.5500000000000003em;margin-left:0;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">s</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:.15em"><span></span></span></span></span></span></span><span class="mclose">]</span></span></span></span>，用户编码器学习用户表示<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>u</mi></mrow><annotation encoding="application/x-tex">u</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:.43056em;vertical-align:0"></span><span class="mord mathnormal">u</span></span></span></span>。NRMS 采用用户级多头部自注意网络和加性注意网络相结合的方法学习用户表征。LSTUR 使用用户 ID 嵌入来捕获用户的短期兴趣，并使用 GRU 网络来捕获用户的长期兴趣。点击预测模型计算每一对用户和候选新闻表示的点击评分<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>𝑠</mi></mrow><annotation encoding="application/x-tex">𝑠</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:.43056em;vertical-align:0"></span><span class="mord mathnormal">s</span></span></span></span>，在 NRMS 和 LSTUR 中均采用点积实现。</p><p>NRMS 和 LSTUR 均采用负采样策略来计算损耗。对于每一条被点击的新闻，在同一印象中对未被点击的新闻<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi></mrow><annotation encoding="application/x-tex">P</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:.68333em;vertical-align:0"></span><span class="mord mathnormal" style="margin-right:.13889em">P</span></span></span></span> 进行采样。对于第<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>𝑃</mi><mo>+</mo><mn>1</mn></mrow><annotation encoding="application/x-tex">𝑃+1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:.76666em;vertical-align:-.08333em"></span><span class="mord mathnormal" style="margin-right:.13889em">P</span><span class="mspace" style="margin-right:.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:.64444em;vertical-align:0"></span><span class="mord">1</span></span></span></span> 个样本，本文将其点击得分表示为<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">{</mo><msub><mi>𝑐</mi><mn>1</mn></msub><mo separator="true">,</mo><msub><mi>𝑐</mi><mn>2</mn></msub><mi mathvariant="normal">.</mi><mi mathvariant="normal">.</mi><mi mathvariant="normal">.</mi><msub><mi>𝑐</mi><mrow><mi>𝑃</mi><mo>+</mo><mn>1</mn></mrow></msub><mo stretchy="false">}</mo></mrow><annotation encoding="application/x-tex">\{𝑐_1,𝑐_2...𝑐_{𝑃+1}\}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-.25em"></span><span class="mopen">{</span><span class="mord"><span class="mord mathnormal">c</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:.15em"><span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:.16666666666666666em"></span><span class="mord"><span class="mord mathnormal">c</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:.15em"><span></span></span></span></span></span></span><span class="mord">.</span><span class="mord">.</span><span class="mord">.</span><span class="mord"><span class="mord mathnormal">c</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:.328331em"><span style="top:-2.5500000000000003em;margin-left:0;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:.13889em">P</span><span class="mbin mtight">+</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:.208331em"><span></span></span></span></span></span></span><span class="mclose">}</span></span></span></span>，其点击标签为<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">{</mo><msub><mi>𝑦</mi><mn>1</mn></msub><mo separator="true">,</mo><msub><mi>𝑦</mi><mn>2</mn></msub><mi mathvariant="normal">.</mi><mi mathvariant="normal">.</mi><mi mathvariant="normal">.</mi><msub><mi>𝑦</mi><mrow><mi>𝑃</mi><mo>+</mo><mn>1</mn></mrow></msub><mo stretchy="false">}</mo></mrow><annotation encoding="application/x-tex">\{𝑦_1,𝑦_2...𝑦_{𝑃+1}\}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-.25em"></span><span class="mopen">{</span><span class="mord"><span class="mord mathnormal" style="margin-right:.03588em">y</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-.03588em;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:.15em"><span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:.16666666666666666em"></span><span class="mord"><span class="mord mathnormal" style="margin-right:.03588em">y</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-.03588em;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:.15em"><span></span></span></span></span></span></span><span class="mord">.</span><span class="mord">.</span><span class="mord">.</span><span class="mord"><span class="mord mathnormal" style="margin-right:.03588em">y</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:.328331em"><span style="top:-2.5500000000000003em;margin-left:-.03588em;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:.13889em">P</span><span class="mbin mtight">+</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:.208331em"><span></span></span></span></span></span></span><span class="mclose">}</span></span></span></span>。第<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>i</mi></mrow><annotation encoding="application/x-tex">i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:.65952em;vertical-align:0"></span><span class="mord mathnormal">i</span></span></span></span> 条新闻的点击概率计算为<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>𝑝</mi><mi>𝑖</mi></msub><mo>=</mo><mi>𝑒</mi><mi>𝑥</mi><mi>𝑝</mi><mo stretchy="false">(</mo><msub><mi>𝑐</mi><mi>𝑖</mi></msub><mo stretchy="false">)</mo><mi mathvariant="normal">/</mi><msubsup><mo>∑</mo><mrow><mi>𝑗</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>𝑃</mi><mo>+</mo><mn>1</mn></mrow></msubsup><mi>𝑒</mi><mi>𝑥</mi><mi>𝑝</mi><mo stretchy="false">(</mo><msub><mi>𝑐</mi><mi>𝑗</mi></msub><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">𝑝_𝑖=𝑒𝑥𝑝(𝑐_𝑖)/\sum^{𝑃+1}_{𝑗=1}𝑒𝑥𝑝(𝑐_𝑗)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:.625em;vertical-align:-.19444em"></span><span class="mord"><span class="mord mathnormal">p</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:0;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:1.417049em;vertical-align:-.43581800000000004em"></span><span class="mord mathnormal">e</span><span class="mord mathnormal">x</span><span class="mord mathnormal">p</span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">c</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:0;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:.15em"><span></span></span></span></span></span></span><span class="mclose">)</span><span class="mord">/</span><span class="mspace" style="margin-right:.16666666666666666em"></span><span class="mop"><span class="mop op-symbol small-op" style="position:relative;top:-.0000050000000000050004em">∑</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:.981231em"><span style="top:-2.40029em;margin-left:0;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:.05724em">j</span><span class="mrel mtight">=</span><span class="mord mtight">1</span></span></span></span><span style="top:-3.2029em;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:.13889em">P</span><span class="mbin mtight">+</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:.43581800000000004em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:.16666666666666666em"></span><span class="mord mathnormal">e</span><span class="mord mathnormal">x</span><span class="mord mathnormal">p</span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">c</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:.311664em"><span style="top:-2.5500000000000003em;margin-left:0;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:.05724em">j</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:.286108em"><span></span></span></span></span></span></span><span class="mclose">)</span></span></span></span>，该样本的损失计算为<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="script">L</mi><mo>=</mo><mtext>−</mtext><msubsup><mo>∑</mo><mrow><mi>𝑖</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>𝑃</mi><mo>+</mo><mn>1</mn></mrow></msubsup><msub><mi>𝑦</mi><mi>𝑖</mi></msub><mo>×</mo><mi>𝑙</mi><mi>𝑜</mi><mi>𝑔</mi><mo stretchy="false">(</mo><msub><mi>𝑝</mi><mi>𝑖</mi></msub><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">\mathcal L=− \sum^{𝑃+1}_{𝑖=1}𝑦_𝑖×𝑙𝑜𝑔(𝑝_𝑖)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:.68333em;vertical-align:0"></span><span class="mord mathcal">L</span><span class="mspace" style="margin-right:.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:1.2809409999999999em;vertical-align:-.29971000000000003em"></span><span class="mord">−</span><span class="mspace" style="margin-right:.16666666666666666em"></span><span class="mop"><span class="mop op-symbol small-op" style="position:relative;top:-.0000050000000000050004em">∑</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:.981231em"><span style="top:-2.40029em;margin-left:0;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">i</span><span class="mrel mtight">=</span><span class="mord mtight">1</span></span></span></span><span style="top:-3.2029em;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:.13889em">P</span><span class="mbin mtight">+</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:.29971000000000003em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:.16666666666666666em"></span><span class="mord"><span class="mord mathnormal" style="margin-right:.03588em">y</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:-.03588em;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:.2222222222222222em"></span><span class="mbin">×</span><span class="mspace" style="margin-right:.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-.25em"></span><span class="mord mathnormal" style="margin-right:.01968em">l</span><span class="mord mathnormal">o</span><span class="mord mathnormal" style="margin-right:.03588em">g</span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">p</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:0;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:.15em"><span></span></span></span></span></span></span><span class="mclose">)</span></span></span></span>。对于良性客户端<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>𝑢</mi><mi>𝑗</mi></msub></mrow><annotation encoding="application/x-tex">𝑢_𝑗</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:.716668em;vertical-align:-.286108em"></span><span class="mord"><span class="mord mathnormal">u</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:.311664em"><span style="top:-2.5500000000000003em;margin-left:0;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:.05724em">j</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:.286108em"><span></span></span></span></span></span></span></span></span></span>，计算其本地数据集中所有样本的总和，定义为<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>𝐿</mi><mi>𝑗</mi></msub><mo>=</mo><msub><mo>∑</mo><mrow><msubsup><mi>𝑠</mi><mi>𝑗</mi><mi>𝑖</mi></msubsup><mo>∈</mo><msub><mi>B</mi><mi>𝑗</mi></msub></mrow></msub><msubsup><mi>𝐿</mi><mi>𝑗</mi><mi>𝑖</mi></msubsup></mrow><annotation encoding="application/x-tex">𝐿_𝑗= \sum_{𝑠^𝑖_𝑗∈B_𝑗}𝐿^𝑖_𝑗</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:.969438em;vertical-align:-.286108em"></span><span class="mord"><span class="mord mathnormal">L</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:.311664em"><span style="top:-2.5500000000000003em;margin-left:0;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:.05724em">j</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:.286108em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:1.447194em;vertical-align:-.62253em"></span><span class="mop"><span class="mop op-symbol small-op" style="position:relative;top:-.0000050000000000050004em">∑</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:.27140999999999993em"><span style="top:-2.40029em;margin-left:0;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathnormal mtight">s</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:.8158857142857143em"><span style="top:-2.177714285714286em;margin-left:0;margin-right:.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mathnormal mtight" style="margin-right:.05724em">j</span></span></span><span style="top:-2.8448em;margin-right:.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:.46117142857142857em"><span></span></span></span></span></span></span><span class="mrel mtight">∈</span><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:.05017em">B</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:.3280857142857143em"><span style="top:-2.357em;margin-left:-.05017em;margin-right:.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mathnormal mtight" style="margin-right:.05724em">j</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:.2818857142857143em"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:.62253em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:.16666666666666666em"></span><span class="mord"><span class="mord mathnormal">L</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:.824664em"><span style="top:-2.441336em;margin-left:0;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:.05724em">j</span></span></span><span style="top:-3.063em;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:.394772em"><span></span></span></span></span></span></span></span></span></span>。损失值<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>𝐿</mi><mi>𝑗</mi></msub></mrow><annotation encoding="application/x-tex">𝐿_𝑗</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:.969438em;vertical-align:-.286108em"></span><span class="mord"><span class="mord mathnormal">L</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:.311664em"><span style="top:-2.5500000000000003em;margin-left:0;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:.05724em">j</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:.286108em"><span></span></span></span></span></span></span></span></span></span>用于计算来自客户端<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>𝑢</mi><mi>𝑗</mi></msub></mrow><annotation encoding="application/x-tex">𝑢_𝑗</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:.716668em;vertical-align:-.286108em"></span><span class="mord"><span class="mord mathnormal">u</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:.311664em"><span style="top:-2.5500000000000003em;margin-left:0;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:.05724em">j</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:.286108em"><span></span></span></span></span></span></span></span></span></span>的更新，其被表示为<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>g</mi><mi>𝑗</mi></msub></mrow><annotation encoding="application/x-tex">g_𝑗</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:.716668em;vertical-align:-.286108em"></span><span class="mord"><span class="mord mathnormal" style="margin-right:.03588em">g</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:.311664em"><span style="top:-2.5500000000000003em;margin-left:-.03588em;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:.05724em">j</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:.286108em"><span></span></span></span></span></span></span></span></span></span>。</p><h1 id="ua-fedrec框架"><a class="anchor" href="#ua-fedrec框架">#</a> UA-FedRec 框架</h1><p>在本小节中，本文将介绍联邦新闻推荐的 UA-FedRec。总体框架如图 1 所示。它由三个核心部分组成：用户模型扰动、新闻相似度扰动和数量扰动。其详细内容如下所述。</p><p><img data-src="https://shun309.oss-cn-hangzhou.aliyuncs.com/photos/20230130175622.png" alt=""></p><p>图 1.UA-FedRec 方法的框架</p><h2 id="用户模型扰动"><a class="anchor" href="#用户模型扰动">#</a> 用户模型扰动</h2><p>用户模型扰动被用于生成对用户模型的恶意更新。在 UA-FedRec 中，本文利用新闻推荐中的先验知识，即新闻推荐的性能高度依赖于用户模型，并以与良性更新相反的方向扰动用户模型的更新。</p><ol><li>首先，本文从恶意客户端设备中的良性数据集估计良性更新。具体来说，对于每个恶意客户端<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>𝑢</mi><mi>𝑖</mi></msub><mo>∈</mo><msub><mi mathvariant="script">U</mi><mi>𝑚</mi></msub></mrow><annotation encoding="application/x-tex">𝑢_𝑖∈\mathcal U_𝑚</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:.6891em;vertical-align:-.15em"></span><span class="mord"><span class="mord mathnormal">u</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:0;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:.2777777777777778em"></span><span class="mrel">∈</span><span class="mspace" style="margin-right:.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:.83333em;vertical-align:-.15em"></span><span class="mord"><span class="mord mathcal" style="margin-right:.09931em">U</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:.151392em"><span style="top:-2.5500000000000003em;margin-left:-.09931em;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:.15em"><span></span></span></span></span></span></span></span></span></span>，本文按照第 3 节中描述的步骤计算一个良性更新。客户端<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>𝑢</mi><mi>𝑖</mi></msub></mrow><annotation encoding="application/x-tex">𝑢_𝑖</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:.58056em;vertical-align:-.15em"></span><span class="mord"><span class="mord mathnormal">u</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:0;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:.15em"><span></span></span></span></span></span></span></span></span></span>的良性用户模型更新被表示为<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msubsup><mi>g</mi><mi>𝑖</mi><mi>𝑢</mi></msubsup></mrow><annotation encoding="application/x-tex">g^𝑢_𝑖</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:.923056em;vertical-align:-.258664em"></span><span class="mord"><span class="mord mathnormal" style="margin-right:.03588em">g</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:.664392em"><span style="top:-2.441336em;margin-left:-.03588em;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span><span style="top:-3.063em;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">u</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:.258664em"><span></span></span></span></span></span></span></span></span></span>。</li><li>然后，本文平均所有恶意客户端的良性用户模型更新以估计良性用户模型更新：𝝁_𝑢=\sum_{1≤𝑖≤𝑚}g^𝑢_𝑖/𝑚。</li><li>其次，本文计算估计的良性用户模型更新的方向s_𝑢=𝑠𝑖𝑔𝑛(𝝁_𝑢)。本文还计算所有恶意客户端的良性用户模型更新的标准差，表示为𝝈𝑢。</li><li>要绕过防御，恶意用户更新不应与良性更新相距太远。为了满足这一要求，来自恶意客户端的恶意更新计算为g^𝑚_𝑢=𝝁_𝑢−\lambda_1 s_𝑢⊙𝝈_𝑢，其中<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>λ</mi><mn>1</mn></msub><mo>≤</mo><mo stretchy="false">[</mo><mn>3</mn><mo separator="true">,</mo><mn>4</mn><mo stretchy="false">]</mo></mrow><annotation encoding="application/x-tex">\lambda_1 ≤ [3,4]</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:.84444em;vertical-align:-.15em"></span><span class="mord"><span class="mord mathnormal">λ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:.2777777777777778em"></span><span class="mrel">≤</span><span class="mspace" style="margin-right:.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-.25em"></span><span class="mopen">[</span><span class="mord">3</span><span class="mpunct">,</span><span class="mspace" style="margin-right:.16666666666666666em"></span><span class="mord">4</span><span class="mclose">]</span></span></span></span>，<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>⊙</mo></mrow><annotation encoding="application/x-tex">⊙</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:.66666em;vertical-align:-.08333em"></span><span class="mord">⊙</span></span></span></span>代表元素间的乘积运算。</li></ol><h2 id="新闻相似性扰动"><a class="anchor" href="#新闻相似性扰动">#</a> 新闻相似性扰动</h2><p>新闻相似性扰动被用于产生对新闻模型的恶意更新。新闻推荐中的先验知识使得新闻建模成为新闻推荐的关键。例如，阅读 &quot;<em> 最佳 PS5 游戏：最值得期待的 PlayStation5 游戏</em> &quot;很可能也会读到&quot;<em> 漫威复仇者联盟的游戏发布日期、新闻、预告片和第一印象</em> &quot;，但不太可能点击&quot;<em> 特朗普在乌克兰战争战壕中冻结援助的代价</em> &quot;。对于一个好的新闻推荐模型，第二新闻的表示应该接近第一新闻在向量空间中的表示，而第三新闻的表示应该远离第一新闻在向量空间中的表示。因此，设计了新闻相似性扰动，使相似新闻的表征更远，不相似新闻的表征更近。</p><p>1. 首先，本文推断新闻表征，并为每条新闻搜索最接近和最远的新闻片段。对于第<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>𝑖</mi></mrow><annotation encoding="application/x-tex">𝑖</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:.65952em;vertical-align:0"></span><span class="mord mathnormal">i</span></span></span></span>条新闻<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>𝑛</mi><mi>𝑖</mi></msub></mrow><annotation encoding="application/x-tex">𝑛_𝑖</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:.58056em;vertical-align:-.15em"></span><span class="mord"><span class="mord mathnormal">n</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:0;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:.15em"><span></span></span></span></span></span></span></span></span></span>，其最近和最远的新闻<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msubsup><mi>𝑛</mi><mi>𝑖</mi><mi>𝑛</mi></msubsup></mrow><annotation encoding="application/x-tex">𝑛^𝑛_𝑖</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:.923056em;vertical-align:-.258664em"></span><span class="mord"><span class="mord mathnormal">n</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:.664392em"><span style="top:-2.441336em;margin-left:0;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span><span style="top:-3.063em;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:.258664em"><span></span></span></span></span></span></span></span></span></span>和<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msubsup><mi>𝑛</mi><mi>𝑖</mi><mi>𝑓</mi></msubsup></mrow><annotation encoding="application/x-tex">𝑛^𝑓_𝑖</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.2438799999999999em;vertical-align:-.276864em"></span><span class="mord"><span class="mord mathnormal">n</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:.9670159999999999em"><span style="top:-2.4231360000000004em;margin-left:0;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span><span style="top:-3.1809080000000005em;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:.10764em">f</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:.276864em"><span></span></span></span></span></span></span></span></span></span>分别计算如下：</p><p><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mtable width="100%"><mtr><mtd width="50%"></mtd><mtd><mtable rowspacing="0.15999999999999992em" columnalign="center" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><msubsup><mi>n</mi><mi>i</mi><mi>f</mi></msubsup><mo>=</mo><mi>m</mi><mi>i</mi><msub><mi>n</mi><mrow><msub><mi>n</mi><mi>j</mi></msub><mo>∈</mo><mi mathvariant="script">N</mi><mo separator="true">,</mo><mi>j</mi><mo mathvariant="normal">≠</mo><mi>i</mi></mrow></msub><msubsup><mi>n</mi><mi>i</mi><mi>T</mi></msubsup><msub><mi>n</mi><mi>j</mi></msub></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><msubsup><mi>n</mi><mi>i</mi><mi>n</mi></msubsup><mo>=</mo><mi>m</mi><mi>a</mi><msub><mi>x</mi><mrow><msub><mi>n</mi><mi>j</mi></msub><mo>∈</mo><mi mathvariant="script">N</mi><mo separator="true">,</mo><mi>j</mi><mo mathvariant="normal">≠</mo><mi>i</mi></mrow></msub><msubsup><mi>n</mi><mi>i</mi><mi>T</mi></msubsup><msub><mi>n</mi><mi>j</mi></msub></mrow></mstyle></mtd></mtr></mtable></mtd><mtd width="50%"></mtd><mtd><mtext>(1)</mtext></mtd></mtr></mtable><annotation encoding="application/x-tex">\begin{array}{c}n_i^f=min_{n_j\in\mathcal{N},j\neq i}n_i^T n_j\\ n_i^n=max_{n_j\in\mathcal{N},j\neq i}n_i^T n_j\end{array}\tag1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:2.528347em;vertical-align:-1.0141735000000003em"></span><span class="mord"><span class="mtable"><span class="arraycolsep" style="width:.5em"></span><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.5141734999999998em"><span style="top:-3.5471575em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathnormal">n</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:.9670159999999999em"><span style="top:-2.4231360000000004em;margin-left:0;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span><span style="top:-3.1809080000000005em;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:.10764em">f</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:.276864em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:.2777777777777778em"></span><span class="mord mathnormal">m</span><span class="mord mathnormal">i</span><span class="mord"><span class="mord mathnormal">n</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:0;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathnormal mtight">n</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:.3280857142857143em"><span style="top:-2.357em;margin-left:0;margin-right:.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mathnormal mtight" style="margin-right:.05724em">j</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:.2818857142857143em"><span></span></span></span></span></span></span><span class="mrel mtight">∈</span><span class="mord mtight"><span class="mord mathcal mtight" style="margin-right:.14736em">N</span></span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight" style="margin-right:.05724em">j</span><span class="mrel mtight"><span class="mrel mtight"><span class="mord vbox mtight"><span class="thinbox mtight"><span class="rlap mtight"><span class="strut" style="height:.8888799999999999em;vertical-align:-.19444em"></span><span class="inner"><span class="mrel mtight"></span></span><span class="fix"></span></span></span></span></span><span class="mrel mtight">=</span></span><span class="mord mathnormal mtight">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:.34731999999999996em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathnormal">n</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:.8413309999999999em"><span style="top:-2.441336em;margin-left:0;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span><span style="top:-3.063em;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:.13889em">T</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:.258664em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathnormal">n</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:.311664em"><span style="top:-2.5500000000000003em;margin-left:0;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:.05724em">j</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:.286108em"><span></span></span></span></span></span></span></span></span><span style="top:-2.3458265em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathnormal">n</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:.664392em"><span style="top:-2.441336em;margin-left:0;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span><span style="top:-3.063em;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:.258664em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:.2777777777777778em"></span><span class="mord mathnormal">m</span><span class="mord mathnormal">a</span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:0;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathnormal mtight">n</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:.3280857142857143em"><span style="top:-2.357em;margin-left:0;margin-right:.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mathnormal mtight" style="margin-right:.05724em">j</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:.2818857142857143em"><span></span></span></span></span></span></span><span class="mrel mtight">∈</span><span class="mord mtight"><span class="mord mathcal mtight" style="margin-right:.14736em">N</span></span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight" style="margin-right:.05724em">j</span><span class="mrel mtight"><span class="mrel mtight"><span class="mord vbox mtight"><span class="thinbox mtight"><span class="rlap mtight"><span class="strut" style="height:.8888799999999999em;vertical-align:-.19444em"></span><span class="inner"><span class="mrel mtight"></span></span><span class="fix"></span></span></span></span></span><span class="mrel mtight">=</span></span><span class="mord mathnormal mtight">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:.34731999999999996em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathnormal">n</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:.8413309999999999em"><span style="top:-2.441336em;margin-left:0;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span><span style="top:-3.063em;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:.13889em">T</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:.258664em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathnormal">n</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:.311664em"><span style="top:-2.5500000000000003em;margin-left:0;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:.05724em">j</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:.286108em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.0141735000000003em"><span></span></span></span></span></span><span class="arraycolsep" style="width:.5em"></span></span></span></span><span class="tag"><span class="strut" style="height:2.528347em;vertical-align:-1.0141735000000003em"></span><span class="mord text"><span class="mord">(</span><span class="mord"><span class="mord">1</span></span><span class="mord">)</span></span></span></span></span></span></p><p>其中<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>n</mi><mi>𝑖</mi></msub></mrow><annotation encoding="application/x-tex">n_𝑖</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:.58056em;vertical-align:-.15em"></span><span class="mord"><span class="mord mathnormal">n</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:0;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:.15em"><span></span></span></span></span></span></span></span></span></span>和<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>n</mi><mi>j</mi></msub></mrow><annotation encoding="application/x-tex">n_j</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:.716668em;vertical-align:-.286108em"></span><span class="mord"><span class="mord mathnormal">n</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:.311664em"><span style="top:-2.5500000000000003em;margin-left:0;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:.05724em">j</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:.286108em"><span></span></span></span></span></span></span></span></span></span> 分别是第𝑖条和第𝑗条新闻的新闻表示。计算所有新闻表示和在每一轮中选择邻居是耗时的。为了降低复杂度，我们假设在<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>𝐾</mi></mrow><annotation encoding="application/x-tex">𝐾</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:.68333em;vertical-align:0"></span><span class="mord mathnormal" style="margin-right:.07153em">K</span></span></span></span>轮中新闻表示之间的距离没有显著变化，从而每隔<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>𝐾</mi></mrow><annotation encoding="application/x-tex">𝐾</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:.68333em;vertical-align:0"></span><span class="mord mathnormal" style="margin-right:.07153em">K</span></span></span></span>轮更新一次所选新闻近邻。此外，本文应用近似最近邻（ANN）来更有效地搜索最近和最远的新闻。</p><p>2. 其次，增大<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>n</mi><mi>𝑖</mi></msub></mrow><annotation encoding="application/x-tex">n _𝑖</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:.58056em;vertical-align:-.15em"></span><span class="mord"><span class="mord mathnormal">n</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:0;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:.15em"><span></span></span></span></span></span></span></span></span></span>与<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msubsup><mi>n</mi><mi>𝑖</mi><mi>𝑛</mi></msubsup></mrow><annotation encoding="application/x-tex">n ^𝑛_ 𝑖</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:.923056em;vertical-align:-.258664em"></span><span class="mord"><span class="mord mathnormal">n</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:.664392em"><span style="top:-2.441336em;margin-left:0;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span><span style="top:-3.063em;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:.258664em"><span></span></span></span></span></span></span></span></span></span>之间的<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>M</mi><mi>S</mi><mi>E</mi></mrow><annotation encoding="application/x-tex">MSE</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:.68333em;vertical-align:0"></span><span class="mord mathnormal" style="margin-right:.10903em">M</span><span class="mord mathnormal" style="margin-right:.05764em">S</span><span class="mord mathnormal" style="margin-right:.05764em">E</span></span></span></span> 损失，减小<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>n</mi><mi>𝑖</mi></msub></mrow><annotation encoding="application/x-tex">n _𝑖</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:.58056em;vertical-align:-.15em"></span><span class="mord"><span class="mord mathnormal">n</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:0;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:.15em"><span></span></span></span></span></span></span></span></span></span>与<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msubsup><mi>n</mi><mi>𝑖</mi><mi>𝑓</mi></msubsup></mrow><annotation encoding="application/x-tex">n ^𝑓 _𝑖</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.2438799999999999em;vertical-align:-.276864em"></span><span class="mord"><span class="mord mathnormal">n</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:.9670159999999999em"><span style="top:-2.4231360000000004em;margin-left:0;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span><span style="top:-3.1809080000000005em;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:.10764em">f</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:.276864em"><span></span></span></span></span></span></span></span></span></span>之间的<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>M</mi><mi>S</mi><mi>E</mi></mrow><annotation encoding="application/x-tex">MSE</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:.68333em;vertical-align:0"></span><span class="mord mathnormal" style="margin-right:.10903em">M</span><span class="mord mathnormal" style="margin-right:.05764em">S</span><span class="mord mathnormal" style="margin-right:.05764em">E</span></span></span></span> 损失。新闻相似度扰动损失计算如下：</p><p><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mtable width="100%"><mtr><mtd width="50%"></mtd><mtd><mrow><msub><mi mathvariant="script">L</mi><mi>n</mi></msub><mo>=</mo><munder><mo>∑</mo><mrow><msub><mi>n</mi><mi>i</mi></msub><mo>∈</mo><mi mathvariant="script">N</mi></mrow></munder><mo stretchy="false">(</mo><msub><mi>n</mi><mi>i</mi></msub><mo>−</mo><msubsup><mi>n</mi><mi>i</mi><mi>f</mi></msubsup><msup><mo stretchy="false">)</mo><mi>T</mi></msup><mo stretchy="false">(</mo><msub><mi>n</mi><mi>i</mi></msub><mo>−</mo><msubsup><mi>n</mi><mi>i</mi><mi>f</mi></msubsup><mo stretchy="false">)</mo><mo>−</mo><mo stretchy="false">(</mo><msub><mi>n</mi><mi>i</mi></msub><mo>−</mo><msubsup><mi>n</mi><mi>i</mi><mi>n</mi></msubsup><msup><mo stretchy="false">)</mo><mi>T</mi></msup><mo stretchy="false">(</mo><msub><mi>n</mi><mi>i</mi></msub><mo>−</mo><msubsup><mi>n</mi><mi>i</mi><mi>n</mi></msubsup><mo stretchy="false">)</mo></mrow></mtd><mtd width="50%"></mtd><mtd><mtext>(2)</mtext></mtd></mtr></mtable><annotation encoding="application/x-tex">\mathcal L_n=\sum_{n_i \in \mathcal N}(n_i-n_i^f)^T(n_i-n_i^f)-(n_i-n_i^n)^T(n_i-n_i^n)\tag2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:.83333em;vertical-align:-.15em"></span><span class="mord"><span class="mord mathcal">L</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:.151392em"><span style="top:-2.5500000000000003em;margin-left:0;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:2.4444410000000003em;vertical-align:-1.394436em"></span><span class="mop op-limits"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.050005em"><span style="top:-1.855664em;margin-left:0"><span class="pstrut" style="height:3.05em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathnormal mtight">n</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:.3280857142857143em"><span style="top:-2.357em;margin-left:0;margin-right:.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:.143em"><span></span></span></span></span></span></span><span class="mrel mtight">∈</span><span class="mord mathcal mtight" style="margin-right:.14736em">N</span></span></span></span><span style="top:-3.0500049999999996em"><span class="pstrut" style="height:3.05em"></span><span><span class="mop op-symbol large-op">∑</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.394436em"><span></span></span></span></span></span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">n</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:0;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:1.2438799999999999em;vertical-align:-.276864em"></span><span class="mord"><span class="mord mathnormal">n</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:.9670159999999998em"><span style="top:-2.4231360000000004em;margin-left:0;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span><span style="top:-3.180908em;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:.10764em">f</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:.276864em"><span></span></span></span></span></span></span><span class="mclose"><span class="mclose">)</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:.8913309999999999em"><span style="top:-3.113em;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:.13889em">T</span></span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">n</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:0;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:1.2438799999999999em;vertical-align:-.276864em"></span><span class="mord"><span class="mord mathnormal">n</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:.9670159999999998em"><span style="top:-2.4231360000000004em;margin-left:0;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span><span style="top:-3.180908em;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:.10764em">f</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:.276864em"><span></span></span></span></span></span></span><span class="mclose">)</span><span class="mspace" style="margin-right:.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-.25em"></span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">n</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:0;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:1.1413309999999999em;vertical-align:-.25em"></span><span class="mord"><span class="mord mathnormal">n</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:.7143919999999999em"><span style="top:-2.4530000000000003em;margin-left:0;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span><span style="top:-3.113em;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:.247em"><span></span></span></span></span></span></span><span class="mclose"><span class="mclose">)</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:.8913309999999999em"><span style="top:-3.113em;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:.13889em">T</span></span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">n</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:0;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-.25em"></span><span class="mord"><span class="mord mathnormal">n</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:.7143919999999999em"><span style="top:-2.4530000000000003em;margin-left:0;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span><span style="top:-3.113em;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:.247em"><span></span></span></span></span></span></span><span class="mclose">)</span></span><span class="tag"><span class="strut" style="height:2.4444410000000003em;vertical-align:-1.394436em"></span><span class="mord text"><span class="mord">(</span><span class="mord"><span class="mord">2</span></span><span class="mord">)</span></span></span></span></span></span></p><p>利用公式 (2) 中的损失通过反向传播算法更新局部模型，得到新闻模型更新<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>g</mi><mi>𝑛</mi></msub></mrow><annotation encoding="application/x-tex">g_ 𝑛</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:.625em;vertical-align:-.19444em"></span><span class="mord"><span class="mord mathnormal" style="margin-right:.03588em">g</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:.151392em"><span style="top:-2.5500000000000003em;margin-left:-.03588em;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:.15em"><span></span></span></span></span></span></span></span></span></span>。为了逃避检测，我们将恶意新闻模型更新的<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>𝐿</mi><mn>2</mn></msub></mrow><annotation encoding="application/x-tex">𝐿_ 2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:.83333em;vertical-align:-.15em"></span><span class="mord"><span class="mord mathnormal">L</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:.15em"><span></span></span></span></span></span></span></span></span></span> 范数与良性新闻模型更新的<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>𝐿</mi><mn>2</mn></msub></mrow><annotation encoding="application/x-tex">𝐿_ 2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:.83333em;vertical-align:-.15em"></span><span class="mord"><span class="mord mathnormal">L</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:.15em"><span></span></span></span></span></span></span></span></span></span> 范数约束得不太远。</p><p>我们按照<strong>如下方式估计良性更新</strong>。对于每个恶意客户端<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>𝑢</mi><mi>𝑖</mi></msub><mo>∈</mo><msub><mi mathvariant="script">U</mi><mi>𝑚</mi></msub></mrow><annotation encoding="application/x-tex">𝑢_𝑖∈\mathcal U_𝑚</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:.6891em;vertical-align:-.15em"></span><span class="mord"><span class="mord mathnormal">u</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:0;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:.2777777777777778em"></span><span class="mrel">∈</span><span class="mspace" style="margin-right:.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:.83333em;vertical-align:-.15em"></span><span class="mord"><span class="mord mathcal" style="margin-right:.09931em">U</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:.151392em"><span style="top:-2.5500000000000003em;margin-left:-.09931em;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:.15em"><span></span></span></span></span></span></span></span></span></span>，我们根据第 3 节描述的步骤，利用其本地良性数据集计算其良性新闻模型更新<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msubsup><mi>g</mi><mi>𝑖</mi><mi>𝑛</mi></msubsup></mrow><annotation encoding="application/x-tex">g ^𝑛_ 𝑖</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:.923056em;vertical-align:-.258664em"></span><span class="mord"><span class="mord mathnormal" style="margin-right:.03588em">g</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:.664392em"><span style="top:-2.441336em;margin-left:-.03588em;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span><span style="top:-3.063em;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:.258664em"><span></span></span></span></span></span></span></span></span></span>。然后计算来自所有恶意客户端的良性更新的<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>𝐿</mi><mn>2</mn></msub></mrow><annotation encoding="application/x-tex">𝐿 _2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:.83333em;vertical-align:-.15em"></span><span class="mord"><span class="mord mathnormal">L</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:.15em"><span></span></span></span></span></span></span></span></span></span> 范数的平均值和标准差，分别记为<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>μ</mi><mi>𝑛</mi></msub></mrow><annotation encoding="application/x-tex">\mu_𝑛</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:.625em;vertical-align:-.19444em"></span><span class="mord"><span class="mord mathnormal">μ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:.151392em"><span style="top:-2.5500000000000003em;margin-left:0;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:.15em"><span></span></span></span></span></span></span></span></span></span>和<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>σ</mi><mi>𝑛</mi></msub></mrow><annotation encoding="application/x-tex">\sigma_𝑛</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:.58056em;vertical-align:-.15em"></span><span class="mord"><span class="mord mathnormal" style="margin-right:.03588em">σ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:.151392em"><span style="top:-2.5500000000000003em;margin-left:-.03588em;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:.15em"><span></span></span></span></span></span></span></span></span></span>。假设良性更新的<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>𝐿</mi><mn>2</mn></msub></mrow><annotation encoding="application/x-tex">𝐿 _2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:.83333em;vertical-align:-.15em"></span><span class="mord"><span class="mord mathnormal">L</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:.15em"><span></span></span></span></span></span></span></span></span></span> 范数服从高斯分布，本文设定恶意新闻模型更新的<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>𝐿</mi><mn>2</mn></msub></mrow><annotation encoding="application/x-tex">𝐿_ 2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:.83333em;vertical-align:-.15em"></span><span class="mord"><span class="mord mathnormal">L</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:.15em"><span></span></span></span></span></span></span></span></span></span> 范数的合理最大值为<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>μ</mi><mi>𝑛</mi></msub><mo>+</mo><msub><mi>λ</mi><mn>2</mn></msub><msub><mi>σ</mi><mi>𝑛</mi></msub></mrow><annotation encoding="application/x-tex">\mu_𝑛 + \lambda_2 \sigma_ 𝑛</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:.7777700000000001em;vertical-align:-.19444em"></span><span class="mord"><span class="mord mathnormal">μ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:.151392em"><span style="top:-2.5500000000000003em;margin-left:0;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:.84444em;vertical-align:-.15em"></span><span class="mord"><span class="mord mathnormal">λ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathnormal" style="margin-right:.03588em">σ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:.151392em"><span style="top:-2.5500000000000003em;margin-left:-.03588em;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:.15em"><span></span></span></span></span></span></span></span></span></span>。最终的恶意新闻模型更新计算为：</p><p><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mtable width="100%"><mtr><mtd width="50%"></mtd><mtd><mrow><msubsup><mi>g</mi><mi>n</mi><mi>m</mi></msubsup><mo>=</mo><mfrac><msub><mi>g</mi><mi>n</mi></msub><mrow><mi>m</mi><mi>a</mi><mi>x</mi><mo stretchy="false">(</mo><mn>1</mn><mo separator="true">,</mo><mi mathvariant="normal">∣</mi><mi mathvariant="normal">∣</mi><msub><mi>g</mi><mi>n</mi></msub><mi mathvariant="normal">∣</mi><msub><mi mathvariant="normal">∣</mi><mn>2</mn></msub><mi mathvariant="normal">/</mi><mo stretchy="false">(</mo><msub><mi>μ</mi><mi>n</mi></msub><mo>+</mo><msub><mi>λ</mi><mn>2</mn></msub><msub><mi>σ</mi><mi>n</mi></msub><mo stretchy="false">)</mo><mo stretchy="false">)</mo></mrow></mfrac></mrow></mtd><mtd width="50%"></mtd><mtd><mtext>(3)</mtext></mtd></mtr></mtable><annotation encoding="application/x-tex">g^m_n=\frac{g_n}{max(1,||g_n||_2/(\mu_n+\lambda_2\sigma_n))}\tag3</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:.9613919999999999em;vertical-align:-.247em"></span><span class="mord"><span class="mord mathnormal" style="margin-right:.03588em">g</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:.7143919999999999em"><span style="top:-2.4530000000000003em;margin-left:-.03588em;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span><span style="top:-3.113em;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:.247em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:2.04356em;vertical-align:-.936em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.1075599999999999em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathnormal">m</span><span class="mord mathnormal">a</span><span class="mord mathnormal">x</span><span class="mopen">(</span><span class="mord">1</span><span class="mpunct">,</span><span class="mspace" style="margin-right:.16666666666666666em"></span><span class="mord">∣</span><span class="mord">∣</span><span class="mord"><span class="mord mathnormal" style="margin-right:.03588em">g</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:.151392em"><span style="top:-2.5500000000000003em;margin-left:-.03588em;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:.15em"><span></span></span></span></span></span></span><span class="mord">∣</span><span class="mord"><span class="mord">∣</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:.15em"><span></span></span></span></span></span></span><span class="mord">/</span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">μ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:.151392em"><span style="top:-2.5500000000000003em;margin-left:0;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:.2222222222222222em"></span><span class="mord"><span class="mord mathnormal">λ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathnormal" style="margin-right:.03588em">σ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:.151392em"><span style="top:-2.5500000000000003em;margin-left:-.03588em;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:.15em"><span></span></span></span></span></span></span><span class="mclose">)</span><span class="mclose">)</span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathnormal" style="margin-right:.03588em">g</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:.151392em"><span style="top:-2.5500000000000003em;margin-left:-.03588em;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:.936em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span><span class="tag"><span class="strut" style="height:2.04356em;vertical-align:-.936em"></span><span class="mord text"><span class="mord">(</span><span class="mord"><span class="mord">3</span></span><span class="mord">)</span></span></span></span></span></span></p><h2 id="数量扰动"><a class="anchor" href="#数量扰动">#</a> 数量扰动</h2><p>在大多数联邦学习方法中，来自不同客户端的更新根据样本大小进行加权平均。为了利用这些先验知识，本文扩大了恶意客户端发送到服务器的样本大小，以放大恶意更新的影响。生成的恶意样本大小应该足够大以增强恶意更新的影响，但也应该足够小以逃避检测。与其他一些联邦学习场景不同，在推荐场景中，样本大小随客户端而变化。本文利用这一特性，通过以下方式扩大恶意客户端的样本大小。将恶意客户端的良性样本大小表示为<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">{</mo><msub><mi>𝑠</mi><mn>1</mn></msub><mo separator="true">,</mo><msub><mi>𝑠</mi><mn>2</mn></msub><mo separator="true">,</mo><mi mathvariant="normal">.</mi><mi mathvariant="normal">.</mi><mi mathvariant="normal">.</mi><msub><mi>𝑠</mi><mi>𝑚</mi></msub><mo stretchy="false">}</mo></mrow><annotation encoding="application/x-tex">\{𝑠_1,𝑠_2, ...𝑠_𝑚\}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-.25em"></span><span class="mopen">{</span><span class="mord"><span class="mord mathnormal">s</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:.15em"><span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:.16666666666666666em"></span><span class="mord"><span class="mord mathnormal">s</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:.15em"><span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:.16666666666666666em"></span><span class="mord">.</span><span class="mord">.</span><span class="mord">.</span><span class="mord"><span class="mord mathnormal">s</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:.151392em"><span style="top:-2.5500000000000003em;margin-left:0;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:.15em"><span></span></span></span></span></span></span><span class="mclose">}</span></span></span></span>。本文计算它们的平均值和标准差，分别表示为<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>μ</mi><mi>s</mi></msub></mrow><annotation encoding="application/x-tex">\mu_s</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:.625em;vertical-align:-.19444em"></span><span class="mord"><span class="mord mathnormal">μ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:.151392em"><span style="top:-2.5500000000000003em;margin-left:0;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">s</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:.15em"><span></span></span></span></span></span></span></span></span></span> 和<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>σ</mi><mi>s</mi></msub></mrow><annotation encoding="application/x-tex">\sigma_s</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:.58056em;vertical-align:-.15em"></span><span class="mord"><span class="mord mathnormal" style="margin-right:.03588em">σ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:.151392em"><span style="top:-2.5500000000000003em;margin-left:-.03588em;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">s</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:.15em"><span></span></span></span></span></span></span></span></span></span>。恶意客户端提交到中心服务器的最终样本量为<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>μ</mi><mi>s</mi></msub><mo>+</mo><msub><mi>λ</mi><mn>3</mn></msub><msub><mi>σ</mi><mi>s</mi></msub></mrow><annotation encoding="application/x-tex">\mu_s + \lambda_3 \sigma_ s</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:.7777700000000001em;vertical-align:-.19444em"></span><span class="mord"><span class="mord mathnormal">μ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:.151392em"><span style="top:-2.5500000000000003em;margin-left:0;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">s</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:.84444em;vertical-align:-.15em"></span><span class="mord"><span class="mord mathnormal">λ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">3</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathnormal" style="margin-right:.03588em">σ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:.151392em"><span style="top:-2.5500000000000003em;margin-left:-.03588em;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">s</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:.15em"><span></span></span></span></span></span></span></span></span></span>，其中<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>0</mn><mo>≤</mo><msub><mi>λ</mi><mn>3</mn></msub><mo>≤</mo><mn>4</mn></mrow><annotation encoding="application/x-tex">0≤\lambda_{3}≤4</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:.78041em;vertical-align:-.13597em"></span><span class="mord">0</span><span class="mspace" style="margin-right:.2777777777777778em"></span><span class="mrel">≤</span><span class="mspace" style="margin-right:.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:.84444em;vertical-align:-.15em"></span><span class="mord"><span class="mord mathnormal">λ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">3</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:.2777777777777778em"></span><span class="mrel">≤</span><span class="mspace" style="margin-right:.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:.64444em;vertical-align:0"></span><span class="mord">4</span></span></span></span>。</p><p>paper：<span class="exturl" data-url="aHR0cHM6Ly9hcnhpdi5vcmcvYWJzLzIyMDIuMDY3MDE=">https://arxiv.org/abs/2202.06701</span></p><p>codes：<span class="exturl" data-url="aHR0cHM6Ly9naXRodWIuY29tL3lqdzEwMjkvVUEtRmVkUmVj">https://github.com/yjw1029/UA-FedRec</span></p><div class="tags"><a href="/tags/%E6%8E%A8%E8%8D%90%E7%B3%BB%E7%BB%9F/" rel="tag"><i class="ic i-tag"></i> 推荐系统</a> <a href="/tags/%E6%96%B0%E9%97%BB%E6%8E%A8%E8%8D%90/" rel="tag"><i class="ic i-tag"></i> 新闻推荐</a> <a href="/tags/%E8%AE%BA%E6%96%87%E7%B2%BE%E8%AF%BB/" rel="tag"><i class="ic i-tag"></i> 论文精读</a> <a href="/tags/%E9%9A%90%E7%A7%81%E4%BF%9D%E6%8A%A4/" rel="tag"><i class="ic i-tag"></i> 隐私保护</a> <a href="/tags/%E6%97%A0%E7%9B%AE%E6%A0%87%E6%94%BB%E5%87%BB/" rel="tag"><i class="ic i-tag"></i> 无目标攻击</a></div></div><footer><div class="meta"><span class="item"><span class="icon"><i class="ic i-calendar-check"></i> </span><span class="text">更新于</span> <time title="修改时间：2023-04-21 14:01:13" itemprop="dateModified" datetime="2023-04-21T14:01:13+08:00">2023-04-21</time> </span><span id="posts/cc988ffe/" class="item leancloud_visitors" data-flag-title="UA-FedRec：对联邦新闻推荐的无目标攻击" title="阅读次数"><span class="icon"><i class="ic i-eye"></i> </span><span class="text">阅读次数</span> <span class="leancloud-visitors-count"></span> <span class="text">次</span></span></div><div class="reward"><button><i class="ic i-heartbeat"></i> 赞赏</button><p>请我喝[茶]~(￣▽￣)~*</p><div id="qr"><div><img data-src="/images/wechatpay.png" alt="hang shun 微信支付"><p>微信支付</p></div><div><img data-src="/images/alipay.png" alt="hang shun 支付宝"><p>支付宝</p></div><div><img data-src="/images/paypal.png" alt="hang shun 贝宝"><p>贝宝</p></div></div></div><div id="copyright"><ul><li class="author"><strong>本文作者： </strong>hang shun <i class="ic i-at"><em>@</em></i>航 順</li><li class="link"><strong>本文链接：</strong> <a href="https://jiang-hs.gitee.io/posts/cc988ffe/" title="UA-FedRec：对联邦新闻推荐的无目标攻击">https://jiang-hs.gitee.io/posts/cc988ffe/</a></li><li class="license"><strong>版权声明： </strong>本站所有文章除特别声明外，均采用 <span class="exturl" data-url="aHR0cHM6Ly9jcmVhdGl2ZWNvbW1vbnMub3JnL2xpY2Vuc2VzL2J5LW5jLXNhLzQuMC9kZWVkLnpo"><i class="ic i-creative-commons"><em>(CC)</em></i>BY-NC-SA</span> 许可协议。转载请注明出处！</li></ul></div></footer></article></div><div class="post-nav"><div class="item left"><a href="/posts/b2c2f458/" itemprop="url" rel="prev" data-background-image="https:&#x2F;&#x2F;pic1.imgdb.cn&#x2F;item&#x2F;60d7f96c5132923bf8a968aa.jpg" title="Adv-MultVAE：基于对抗学习的隐私保护推荐算法"><span class="type">上一篇</span> <span class="category"><i class="ic i-flag"></i> 隐私保护新闻推荐</span><h3>Adv-MultVAE：基于对抗学习的隐私保护推荐算法</h3></a></div><div class="item right"><a href="/posts/ef078385/" itemprop="url" rel="next" data-background-image="https:&#x2F;&#x2F;pic1.imgdb.cn&#x2F;item&#x2F;60d7f97b5132923bf8a9b545.jpg" title="FedNewsRec：隐私保护新闻推荐模型学习"><span class="type">下一篇</span> <span class="category"><i class="ic i-flag"></i> 联邦学习</span><h3>FedNewsRec：隐私保护新闻推荐模型学习</h3></a></div></div><div class="wrap" id="comments"></div></div><div id="sidebar"><div class="inner"><div class="panels"><div class="inner"><div class="contents panel pjax" data-title="文章目录"><ol class="toc"><li class="toc-item toc-level-1"><a class="toc-link" href="#%E9%97%AE%E9%A2%98%E8%A1%A8%E8%BF%B0"><span class="toc-number">1.</span> <span class="toc-text">问题表述</span></a></li><li class="toc-item toc-level-1"><a class="toc-link" href="#%E5%A8%81%E8%83%81%E6%A8%A1%E5%9E%8B"><span class="toc-number">2.</span> <span class="toc-text">威胁模型</span></a></li><li class="toc-item toc-level-1"><a class="toc-link" href="#%E5%9F%BA%E6%9C%AC%E6%96%B0%E9%97%BB%E6%8E%A8%E8%8D%90%E6%A8%A1%E5%9E%8B"><span class="toc-number">3.</span> <span class="toc-text">基本新闻推荐模型</span></a></li><li class="toc-item toc-level-1"><a class="toc-link" href="#ua-fedrec%E6%A1%86%E6%9E%B6"><span class="toc-number">4.</span> <span class="toc-text">UA-FedRec 框架</span></a><ol class="toc-child"><li class="toc-item toc-level-2"><a class="toc-link" href="#%E7%94%A8%E6%88%B7%E6%A8%A1%E5%9E%8B%E6%89%B0%E5%8A%A8"><span class="toc-number">4.1.</span> <span class="toc-text">用户模型扰动</span></a></li><li class="toc-item toc-level-2"><a class="toc-link" href="#%E6%96%B0%E9%97%BB%E7%9B%B8%E4%BC%BC%E6%80%A7%E6%89%B0%E5%8A%A8"><span class="toc-number">4.2.</span> <span class="toc-text">新闻相似性扰动</span></a></li><li class="toc-item toc-level-2"><a class="toc-link" href="#%E6%95%B0%E9%87%8F%E6%89%B0%E5%8A%A8"><span class="toc-number">4.3.</span> <span class="toc-text">数量扰动</span></a></li></ol></li></ol></div><div class="related panel pjax" data-title="系列文章"><ul><li><a href="/posts/b2c2f458/" rel="bookmark" title="Adv-MultVAE：基于对抗学习的隐私保护推荐算法">Adv-MultVAE：基于对抗学习的隐私保护推荐算法</a></li><li><a href="/posts/f8ce3000/" rel="bookmark" title="Hetedp：基于异构图神经网络的隐私保护推荐">Hetedp：基于异构图神经网络的隐私保护推荐</a></li><li class="active"><a href="/posts/cc988ffe/" rel="bookmark" title="UA-FedRec：对联邦新闻推荐的无目标攻击">UA-FedRec：对联邦新闻推荐的无目标攻击</a></li><li><a href="/posts/ef078385/" rel="bookmark" title="FedNewsRec：隐私保护新闻推荐模型学习">FedNewsRec：隐私保护新闻推荐模型学习</a></li><li><a href="/posts/d414c6e0/" rel="bookmark" title="Efficient-FedRec：高效的新闻推荐隐私保护框架">Efficient-FedRec：高效的新闻推荐隐私保护框架</a></li><li><a href="/posts/e3b95b70/" rel="bookmark" title="Fastformer：Additive Attention Can Be All You Need">Fastformer：Additive Attention Can Be All You Need</a></li></ul></div><div class="overview panel" data-title="站点概览"><div class="author" itemprop="author" itemscope itemtype="http://schema.org/Person"><img class="image" itemprop="image" alt="hang shun" data-src="/images/avatar.jpg"><p class="name" itemprop="name">hang shun</p><div class="description" itemprop="description">世中逢尔，雨中逢花</div></div><nav class="state"><div class="item posts"><a href="/archives/"><span class="count">45</span> <span class="name">文章</span></a></div><div class="item categories"><a href="/categories/"><span class="count">10</span> <span class="name">分类</span></a></div><div class="item tags"><a href="/tags/"><span class="count">25</span> <span class="name">标签</span></a></div></nav><div class="social"><span class="exturl item github" data-url="aHR0cHM6Ly9naXRodWIuY29tL0pJQU5HLUhT" title="https:&#x2F;&#x2F;github.com&#x2F;JIANG-HS"><i class="ic i-github"></i></span> <span class="exturl item zhihu" data-url="aHR0cHM6Ly93d3cuemhpaHUuY29tL3Blb3BsZS9odWktc2h1bi14aW4tbGl1" title="https:&#x2F;&#x2F;www.zhihu.com&#x2F;people&#x2F;hui-shun-xin-liu"><i class="ic i-zhihu"></i></span> <span class="exturl item music" data-url="aHR0cHM6Ly9tdXNpYy4xNjMuY29tLyMvdXNlci9ob21lP2lkPTE4MzkwMTczMzI=" title="https:&#x2F;&#x2F;music.163.com&#x2F;#&#x2F;user&#x2F;home?id&#x3D;1839017332"><i class="ic i-cloud-music"></i></span> <span class="exturl item bilibili" data-url="aHR0cHM6Ly9zcGFjZS5iaWxpYmlsaS5jb20vMzIxMTYyNDg1" title="https:&#x2F;&#x2F;space.bilibili.com&#x2F;321162485"><i class="ic i-bilibili"></i></span></div><ul class="menu"><li class="item"><a href="/" rel="section"><i class="ic i-home"></i>首页</a></li><li class="item"><a href="/about/" rel="section"><i class="ic i-user"></i>关于</a></li><li class="item dropdown"><a href="javascript:void(0);"><i class="ic i-feather"></i>文章</a><ul class="submenu"><li class="item"><a href="/archives/" rel="section"><i class="ic i-list-alt"></i>归档</a></li><li class="item"><a href="/categories/" rel="section"><i class="ic i-th"></i>分类</a></li><li class="item"><a href="/tags/" rel="section"><i class="ic i-tags"></i>标签</a></li></ul></li><li class="item"><a href="/friends/" rel="section"><i class="ic i-heart"></i>友達</a></li><li class="item"><a href="/movie/" rel="section"><i class="ic i-play"></i>movie</a></li><li class="item"><a href="/music/" rel="section"><i class="ic i-music"></i>music</a></li></ul></div></div></div><ul id="quick"><li class="prev pjax"><a href="/posts/b2c2f458/" rel="prev" title="上一篇"><i class="ic i-chevron-left"></i></a></li><li class="up"><i class="ic i-arrow-up"></i></li><li class="down"><i class="ic i-arrow-down"></i></li><li class="next pjax"><a href="/posts/ef078385/" rel="next" title="下一篇"><i class="ic i-chevron-right"></i></a></li><li class="percent"></li></ul></div></div><div class="dimmer"></div></div></main><footer id="footer"><div class="inner"><div class="widgets"><div class="rpost pjax"><h2>随机文章</h2><ul><li class="item"><div class="breadcrumb"><a href="/categories/%E8%AE%BA%E6%96%87%E7%B2%BE%E8%AF%BB/" title="分类于 论文精读">论文精读</a> <i class="ic i-angle-right"></i> <a href="/categories/%E8%AE%BA%E6%96%87%E7%B2%BE%E8%AF%BB/%E6%96%B0%E9%97%BB%E6%8E%A8%E8%8D%90/" title="分类于 新闻推荐">新闻推荐</a></div><span><a href="/posts/82023bca/" title="NRMS：基于多头自注意力的神经新闻推荐">NRMS：基于多头自注意力的神经新闻推荐</a></span></li><li class="item"><div class="breadcrumb"></div><span><a href="/posts/67decac2/" title="初识GCN">初识GCN</a></span></li><li class="item"><div class="breadcrumb"></div><span><a href="/posts/6a16b017/" title="51单片机基础-4">51单片机基础-4</a></span></li><li class="item"><div class="breadcrumb"></div><span><a href="/posts/d2c59692/" title="PyTorch自动微分Autograd">PyTorch自动微分Autograd</a></span></li><li class="item"><div class="breadcrumb"><a href="/categories/%E8%AE%BA%E6%96%87%E7%B2%BE%E8%AF%BB/" title="分类于 论文精读">论文精读</a> <i class="ic i-angle-right"></i> <a href="/categories/%E8%AE%BA%E6%96%87%E7%B2%BE%E8%AF%BB/%E6%96%B0%E9%97%BB%E6%8E%A8%E8%8D%90/" title="分类于 新闻推荐">新闻推荐</a> <i class="ic i-angle-right"></i> <a href="/categories/%E8%AE%BA%E6%96%87%E7%B2%BE%E8%AF%BB/%E6%96%B0%E9%97%BB%E6%8E%A8%E8%8D%90/%E9%9A%90%E7%A7%81%E4%BF%9D%E6%8A%A4%E6%96%B0%E9%97%BB%E6%8E%A8%E8%8D%90/" title="分类于 隐私保护新闻推荐">隐私保护新闻推荐</a> <i class="ic i-angle-right"></i> <a href="/categories/%E8%81%94%E9%82%A6%E5%AD%A6%E4%B9%A0/" title="分类于 联邦学习">联邦学习</a></div><span><a href="/posts/d414c6e0/" title="Efficient-FedRec：高效的新闻推荐隐私保护框架">Efficient-FedRec：高效的新闻推荐隐私保护框架</a></span></li><li class="item"><div class="breadcrumb"><a href="/categories/%E6%9C%BA%E5%99%A8%E5%AD%A6%E4%B9%A0%E5%9F%BA%E7%A1%80/" title="分类于 机器学习基础">机器学习基础</a></div><span><a href="/posts/202f1f0f/" title="梯度下降及线性回归">梯度下降及线性回归</a></span></li><li class="item"><div class="breadcrumb"><a href="/categories/%E8%AE%BA%E6%96%87%E7%B2%BE%E8%AF%BB/" title="分类于 论文精读">论文精读</a> <i class="ic i-angle-right"></i> <a href="/categories/%E8%AE%BA%E6%96%87%E7%B2%BE%E8%AF%BB/%E6%96%B0%E9%97%BB%E6%8E%A8%E8%8D%90/" title="分类于 新闻推荐">新闻推荐</a></div><span><a href="/posts/febd3949/" title="提示学习新闻推荐">提示学习新闻推荐</a></span></li><li class="item"><div class="breadcrumb"></div><span><a href="/posts/321bfdac/" title="融合商品潜在互补性发现学习笔记">融合商品潜在互补性发现学习笔记</a></span></li><li class="item"><div class="breadcrumb"><a href="/categories/%E6%9C%BA%E5%99%A8%E5%AD%A6%E4%B9%A0%E5%9F%BA%E7%A1%80/" title="分类于 机器学习基础">机器学习基础</a></div><span><a href="/posts/20417848/" title="循环神经网络">循环神经网络</a></span></li><li class="item"><div class="breadcrumb"><a href="/categories/%E8%AE%BA%E6%96%87%E7%B2%BE%E8%AF%BB/" title="分类于 论文精读">论文精读</a> <i class="ic i-angle-right"></i> <a href="/categories/%E8%AE%BA%E6%96%87%E7%B2%BE%E8%AF%BB/%E6%96%B0%E9%97%BB%E6%8E%A8%E8%8D%90/" title="分类于 新闻推荐">新闻推荐</a> <i class="ic i-angle-right"></i> <a href="/categories/%E8%AE%BA%E6%96%87%E7%B2%BE%E8%AF%BB/%E6%96%B0%E9%97%BB%E6%8E%A8%E8%8D%90/%E9%9A%90%E7%A7%81%E4%BF%9D%E6%8A%A4%E6%96%B0%E9%97%BB%E6%8E%A8%E8%8D%90/" title="分类于 隐私保护新闻推荐">隐私保护新闻推荐</a> <i class="ic i-angle-right"></i> <a href="/categories/%E8%81%94%E9%82%A6%E5%AD%A6%E4%B9%A0/" title="分类于 联邦学习">联邦学习</a></div><span><a href="/posts/ef078385/" title="FedNewsRec：隐私保护新闻推荐模型学习">FedNewsRec：隐私保护新闻推荐模型学习</a></span></li></ul></div><div><h2>最新评论</h2><ul class="leancloud-recent-comment"></ul></div></div><div class="status"><div class="copyright">&copy; 2020 – <span itemprop="copyrightYear">2023</span> <span class="with-love"><i class="ic i-sakura rotate"></i> </span><span class="author" itemprop="copyrightHolder">hang shun @ hang shun</span></div><div class="count"><span class="post-meta-item-icon"><i class="ic i-chart-area"></i> </span><span title="站点总字数">267k 字</span> <span class="post-meta-divider">|</span> <span class="post-meta-item-icon"><i class="ic i-coffee"></i> </span><span title="站点阅读时长">4:02</span></div><div class="powered-by">基于 <span class="exturl" data-url="aHR0cHM6Ly9oZXhvLmlv">Hexo</span> & Theme.<span class="exturl" data-url="aHR0cHM6Ly9naXRodWIuY29tL2FtZWhpbWUvaGV4by10aGVtZS1zaG9rYQ==">Shoka</span></div></div></div></footer></div><script data-config type="text/javascript">var LOCAL={path:"posts/cc988ffe/",favicon:{show:"(´Д｀)被发现了！",hide:"（●´3｀●）我藏好了~"},search:{placeholder:"文章搜索",empty:"关于 「 ${query} 」，什么也没搜到",stats:"${time} ms 内找到 ${hits} 条结果"},valine:!0,copy_tex:!0,katex:!0,fancybox:!0,copyright:'复制成功，转载请遵守 <i class="ic i-creative-commons"></i>BY-NC-SA 协议。',ignores:[function(e){return e.includes("#")},function(e){return new RegExp(LOCAL.path+"$").test(e)}]}</script><script src="https://cdn.polyfill.io/v2/polyfill.js"></script><script src="//cdn.jsdelivr.net/combine/npm/pace-js@1.0.2/pace.min.js,npm/pjax@0.2.8/pjax.min.js,npm/whatwg-fetch@3.4.0/dist/fetch.umd.min.js,npm/animejs@3.2.0/lib/anime.min.js,npm/algoliasearch@4/dist/algoliasearch-lite.umd.js,npm/instantsearch.js@4/dist/instantsearch.production.min.js,npm/lozad@1/dist/lozad.min.js,npm/quicklink@2/dist/quicklink.umd.js"></script><script src="/js/app.js?v=0.0.0"></script></body></html><!-- rebuild by hrmmi -->